An air source constantly increases the air supply rate of a balloon. The volume V in cubic feet is given by V(t) = 6t + 1, [0 $\le$ t $\le$ 5], where t is time in seconds. How fast is the volume of the balloon increasing at t = 5s? A) 30 ft³/s B) 31 ft³/s C) 1 ft³/s D) 0 ft³/s E) 6 ft³/s

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Quizplus · Accepted Answer

The rate of increase of the balloon's volume is given by the derivative of V(t) with respect to t, which is V'(t) = 6. This rate is constant and does not depend on the value of t, so at t = 5s, the volume is increasing at a rate of 6 cubic feet per second.

An Air Source Constantly Increases the Air Supply Rate of a Balloon